As a preamble, due that this is very small, I used a tinypico.com ESP32. I took the steps done by Unexpected maker to turn off the Dotstar led so it consumes as less as possible in deepsleep (My measurement 0.08 mA)

With a Lipo battery of 80 mA tt has been working since Friday 11:30 am (146 hrs aprox.)
If my maths are not wrong 80/146 is approx. 0.54 mA per hour consumption. Updating every 4 mins the epaper and WiFi sync only once per day less than 2 secs online using esp32 tinypico.

3D model ready for the printer:

https://www.thingiverse.com/thing:4546700

Smallest epaper option that I used is an Heltec 1.54 inches (200x200) Please note that at the moment I'm not measuring battery level, when it's over it will simply not update anymore, and you may see small droplets of black in the epaper (Current is not enough to turn it full black I guess) This is how it looked when it stopped:

I cannot guarantee that it will last that much, but provided connects only one per day to sync, then it should consume only what the epaper needs to refresh and go again to sleep.

Repository is the same just in branch refactor/oop:
https://github.com/martinberlin/cale-idf/tree/refactor/oop/main
C++ source: demo-sleep-clock-v2.cpp
Happy builds!